The salaries and all other expenses of the personnel board, the personnel director, and all others arising under the provisions hereof, unless otherwise herein provided, shall be paid by warrants drawn by the personnel board and signed by at least two members thereof on the general fund of the county. At the end of the county’s fiscal year it shall prorate the total sum which it has expended for the purposes of this part between itself and the cities and appointing authorities subject to this part, charging each with such part of the total sum so expended as the total number of employees of such county, city, or appointing authority who were subject to this part on the last day of the county’s fiscal year bears to the total number of employees of all appointing authorities subject to this part on such last day of the county’s fiscal year. The sum so arrived at by the county as the proper contribution of each shall be certified to the director of personnel and when approved by him or her in writing, shall become a liability of the respective county, city, and appointing authorities and shall be paid immediately to the county. In the event the salaries of a county, city, or an appointing authority are paid in part from different treasuries or different funds, in the same treasury, the liability for this contribution shall accrue against such various treasuries or funds in the same proportion, as the salaries of the employees of the county, city, or the appointing authorities are paid therefrom. In the event any contribution levied hereunder shall not be paid within 30 days after approval by the personnel director, the county may bring suit therefor in any court of competent jurisdiction and any judgment so recovered shall be satisfied from any funds in such treasury or funds against which such contribution levy lies.